What is a proper non-trivial ideal? 
Corollary: Let F be a field, Then, F has no proper non-trivial ideals.

I apologise for this trivial question. What exactly is a proper non-trivial ideal? Well, non-trivial is defined as not the zero-set.
What about proper?
Thanks in advance.
 A: The most ordinary convention, as far as I know, is that proper means "not $R$," and nonzero means "not $\{0\}$," and that nontrivial means "not $R$ and not $\{0\}$"*.
Your author could adhere to other conventions, of course, and I have seen "trivial" synonymously used as "nonzero." Examine the text to see if it is defined precisely.

See for example http://www.math.uiuc.edu/~r-ash/Algebra/Chapter2.pdf definition 2.2.3.
A: Proper ideal: $\;I<F\;,\;\;I\neq F\;$ . Non trivial: $\;I\neq\{0\}\;$
A: proper means its not the whole ring. If a field were to have a nontrivial (i.e. nonzero) proper (i.e. not equal to the whole ring) ideal $I$, then since $I$ is nonempty, it contains something, say $x$. And since $I$ is nontrivial, its safe to assume that $x\ne 0$. But then $x$ has an inverse in the field, say $yx=1$. But then $yx$ is in $I$. Therefore $1$ is in $I$. But now everything is in I because any ideal which contains unity is the whole ring. 
A: An ideal I of the ring A is said to be proper iff I is not trivial iff the ideal I is both different from {0] and A. Thus, if A is a field, then A contains no proper ideal .
